Lady matriarch running a London landmark (9,4)
I believe the answer is:
admiralty arch
'a london landmark' is the definition.
(structure in central London)
'lady matriarch running' is the wordplay.
'running' indicates an anagram.
'lady'+'matriarch'='ladymatriarch'
'ladymatriarch' with letters rearranged gives 'ADMIRALTY ARCH'.
(Other definitions for admiralty arch that I've seen before include "Building between The Mall and Trafalgar Square" , "London landmark between The Mall and Trafalgar Square" , "It stands at the Trafalgar Sq. end of the Mall" , "Feature over The Mall" , "Entrance to The Mall off Trafalgar Square" .)